A327605 Number of parts in all twice partitions of n where both partitions are strict.

0, 1, 1, 5, 8, 15, 28, 49, 86, 156, 259, 412, 679, 1086, 1753, 2826, 4400, 6751, 10703, 16250, 24757, 38047, 57459, 85861, 129329, 192660, 286177, 424358, 624510, 915105, 1347787, 1961152, 2847145, 4144089, 5988205, 8638077, 12439833, 17837767, 25536016

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Example

a(3) = 5 = 1+2+2 counting the parts in 3, 21, 2|1.

Maple

g:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
      `if`(n=0, [1, 0], g(n, i-1) +(f-> f+
       [0, f[1]])(g(n-i, min(n-i, i-1)))))
    end:
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
      `if`(n=0, [1, 0], b(n, i-1) +(h-> (f-> f+[0, f[1]*
       h[2]/h[1]])(b(n-i, min(n-i, i-1))*h[1]))(g(i$2))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..42);

Mathematica

b[n_, i_, k_] := b[n, i, k] = With[{}, If[n == 0, Return@{1, 0}]; If[k == 0, Return@{1, 1}]; If[i (i + 1)/2 < n, Return@{0, 0}]; b[n, i - 1, k] + Function[h, Function[f, f + {0, f[[1]] h[[2]]/h[[1]]}][h[[1]] b[n - i, Min[n - i, i - 1], k]]][b[i, i, k - 1]]];
a[n_] := b[n, n, 2][[2]];
a /@ Range[0, 42] (* Jean-François Alcover, Jun 03 2020, after Alois P. Heinz in A327622 *)

Crossrefs

Cf. A000009, A279785, A327553, A327594, A327607, A327608, A327795.

Column k=2 of A327622.

Sequence in context: A233186 A314559 A314560 * A259724 A259585 A220034

Adjacent sequences: A327602 A327603 A327604 * A327606 A327607 A327608

Keyword

nonn

Author

Alois P. Heinz, Sep 18 2019

Status

approved